Atoms, Molecules and Optical Physics 2 pp 625-666 | Cite as

# Optical Bloch Equations

## Abstract

To set the stage, in Sect. 10.1 we take a look onto an experiment from modern quantum optics. In Sect. 10.2 the important “dressed state” model is introduced to analyze the two level system in a quasi-monochromatic light. Section 10.3 presents several characteristic experiments which may be explained effortless with this model. Section 10.4 derives the theoretical framework for treating such systems quantitatively, starting with the fundamental Liouville-von-Neumann equation from which the “Optical Bloch equations” are derived. In Sect. 10.5 we apply these to a number of important questions which in earlier chapters could only be discussed by hand waving arguments. On these grounds, Sect. 10.6 develops some basics of short pulse spectroscopy. Finally, Sect. 10.7 introduces a somewhat more complex application, the STIRAP method, today of increasing interest also in the context of “quantum information”.

## Keywords

Laser Field Rabi Frequency Rotate Wave Approximation Population Transfer Excitation Probability## Notes

## Acronyms and Terminology

‘complex conjugate’.

‘Continuous wave’, (as opposed to pulsed) light beam, laser radiation etc.

‘Electric dipole’, transitions induced by the interaction of an electric dipole with the electric field component of electromagnetic radiation.

‘Electron paramagnetic resonance’, spectroscopy, also called *electron spin resonance* ESR (see Sect. 9.5.2 in Vol. 1).

‘Far-off-resonance optical dipole trap’, for trapping single atoms; a typical setup is shown in Fig. 10.1.

‘Fabry-Pérot interferometer’, for high precision spectroscopy and laser resonators (see Sect. 6.1.2 in Vol. 1).

‘Full width at half maximum’.

‘Hanbury Brown and Twiss’, experiment, to determine the lateral correlation of light by a second-order interferometric measurement (see Sect. 2.1.6).

‘Magneto optical trap’, for a typical setup see e.g. Fig. 6.26.

‘National institute of standards and technology’, located at Gaithersburg (MD) and Boulder (CO), USA. http://www.nist.gov/index.html.

‘Nuclear magnetic resonance’, spectroscopy, a rather universal spectroscopic method for identifying molecules (see Sect. 9.5.3 in Vol. 1).

‘Ordinary differential equation’.

‘Rotating wave approximation’, allows to solve the coupled equations for a two level system in a strong electromagnetic field in closed analytical form (see Sect. 10.2.3).

‘Stimulated Raman adiabatic passage’, special type of optical pumping, see Sect. 10.7.

‘Ultraviolet’, spectral range of electromagnetic radiation. Wavelengths between 100 nm and 400 nm according to ISO 21348 (2007).

‘Vacuum ultraviolet’, spectral range of electromagnetic radiation. part of the UV spectral range. Wavelengths between 10 nm and 200 nm according to ISO 21348 (2007).

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